| Research Abstract |
i) In the past we developed the general theory relating the hydrodynamic system and the Boltzmann system in a steady flow of a slightly rarefied gas past bodies. The explicit data of the slip coefficient and Knudsen layer correction, however, were given only for the BKW model equation. In this study, developing a new method of numerical analysis of the standard Boltzmann equation, we analyzed the slip coefficient and the Knudsen layer for a hard-sphere molecular gas and completed the general theory.
ii) The thermal transpiration flow and the flow induced between noncoaxial circular cylinders with different temperatures were analyzed for the whole range of the Knudsen number. These are typical flows of rarefied gas induced by temperature field in the absence of external forces, which are not seen in a continuum gas. The force on the cylinder shows an interesting feature as a function of the Knudsen number.
iii) The transient behavior of an initially uniform gas bounded by its plane conden
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sed phase was investigated in detail by the kinetic theory when evaporation took place. From the long-time solution the steady behavior of the gas, as well as the relation among the variables at infinity and on the condensed phase, was clarified. This provides the boundary condition for the fluiddynamic equation on the interface between a gas and its condensed phase. Further, steady evaporation flows from a circular cylinder was analyzed accurately for a wide range of the rate of evaporation and the Knudsen number. The discontinuity of the velocity distribution function in gas was first analyzed accurately in this study.
iv) In the course of these studies, we proposed several new methods of analysis of the kinetic equation, such as the numerical kernel method, the method of analyzing the discontinuity of the velocity distribution function, the modified Knudsen number expansion method, and the modified Neumann series method for infinite domain problems.
v) Applying our new methods, we made accurate analyses of various fundamental rarefied gas flows for the whole range of gas rarefaction, such as the Couette flow, the Poiseuille flow, a flow through a slit, nonlinear wave propagation, and the heat transfer between two plates. Less
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